from manim import *
class CustomCurve(VMobject):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        # 定义自定义曲线的控制点
        points = [
            [5, 3, 0],
            [3,-3,0],
            [0,-5,0],
            [3,-7,0],
            [5,-13,0],
        ]
        self.set_points_smoothly(points)
class CustomCurve1(VMobject):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        # 定义自定义曲线的控制点
        points = [
            [18, 4, 0],
            [22,-12,0],
            [43,-16,0]
        ]
        self.set_points_smoothly(points)

class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(6*2+1):       
            dot1=Dot([-50,5*(i-6),0]).set_opacity(0.5)
            dot2=Dot([50,5*(i-6),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(10*2+1):        
            dot3=Dot([(i-10)*5,-30,0]).set_opacity(0.5)
            dot4=Dot([(i-10)*5,30,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #镜头跟进效果 
        self.camera.frame.save_state()
         #题目出现
        text = Tex(r"\text{(张1000题2)若反常积分$\int _{0}^{+\infty }\dfrac{\ln x}{\left( 1+x\right) x^{1-p}}dx$\text{收敛,则}}"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,20,0])
        text1 = Tex(
                   r"\text{(A)}$p<1$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-22,15,0])
        text2 = Tex(
                    r"\text{(B)}$p>1$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([22,15,0])
        text3 = Tex(
                   r"\text{(C)}$0<p<1$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-22,8,0])
        text4 = Tex(
                    r"\text{(D)}$0\leq p <1$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([22,8,0])

        self.play(Write(text),Write(text1),Write(text2),Write(text3),Write(text4))
        self.wait(0.1)
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
        #self.play(text.animate().move_to([0,20,0]),text1.animate().move_to([-22,15,0]) ,text2.animate().move_to([22,15,0]),text3.animate().move_to([-22,8,0]),text4.animate().move_to([22,8,0]) )

        text1 = Tex(
                    r"\text{瑕点为}$+\infty $\text{和}$0$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-36,0,0])
        self.play(Write(text1))
        text2 = Tex(
                    r"\text{当}$x\rightarrow +\infty $",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-40,-5,0])
        self.play(Write(text2))
        text3 = Tex(
                    r"$\dfrac{\ln x}{\left( 1+x\right) x^{1-p}}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-25,-5,0])
        self.play(Write(text3))
        text4 = Tex(
                    r"\text{等价于}$\dfrac{\ln x}{x^{2-p}}$",color=PURPLE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,-5,0])
        self.play(Write(text4))
        rectangle=Rectangle(color=BLUE,fill_opacity=0.0,width=13,height=8
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle.move_to([-10, -5, 0])
        self.play(Create(rectangle))
        #画曲线
        curve = CustomCurve(color=RED, stroke_width=20)
        
        # 添加到场景并播放动画
        self.play(Create(curve))
        self.wait(0.5)





        text5 = Tex(
                    r"$2-p>1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([13, 3, 0])
        
        text6 = Tex(
                    r"$2-p=1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([13,-5,0])
        text7 = Tex(
                    r"$2-p<1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([13,-13,0])
        
        text8 = Tex(
                    r"$x\gg \ln x$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([-20,-15,0])



        self.play(Write(text5),Write(text6),Write(text7))

        self.play(Write(text8))

        text9 = Tex(
                    r"\text{与}$\dfrac{1}{x^{2-p}}$\text{同趋势}",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([27, 3, 0])
        self.play(Write(text9))
        text11 = Tex(
                    r"\text{(收敛)}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([40,3,0])
        self.play(Write(text11))

        text12 = Tex(
                    r"\text{与}$\dfrac{1}{x^{2-p}}$\text{同趋势}",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([27, -13, 0])
        self.play(Write(text12),FadeOut(text8))
        text13 = Tex(
                    r"\text{(发散)}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([40,-13,0])
        self.play(Write(text13))
        
        text14 = Tex(
                    r"$\int _{1}^{+\infty }\dfrac{\ln x}{x}dx$",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        self.play(Write(text14))
        text15 = Tex(
                    r"$\int ^{+\infty }_{1}\ln xdlnx$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        text16 = Tex(
                    r"$\int _{0}^{+\infty }tdt$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        self.play(
            ReplacementTransform(text14,text15)
        )
        self.wait(0.5)
        self.play(
            
            ReplacementTransform(text15,text16)
        )
        text17 = Tex(
                    r"$\text{(发散)}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,-15,0])
        self.play(Write(text17))
        self.wait(0.5)
        text18 = Tex(
                    r"$\text{(发散)}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([30,-5,0])
        self.play(Write(text18))
        text19 = Tex(
                    r"$p<1$",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,12,0])
        self.play(Write(text19))
        self.wait(0.5)
        self.play(Uncreate(text18),Uncreate(text17),Uncreate(text16),Uncreate(text13)
                  ,Uncreate(text12),Uncreate(text11),Uncreate(text9)
                  ,Uncreate(text8),Uncreate(text7),Uncreate(text6)
                  ,Uncreate(text5),Uncreate(text4),Uncreate(text3)
                  ,Uncreate(text2),Uncreate(curve),FadeOut(rectangle))
        




        text2 = Tex(
                    r"\text{当}$x\rightarrow 0$",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-40,-5,0])
        self.play(Write(text2))
        text3 = Tex(
                    r"$\dfrac{\ln x}{\left( 1+x\right) x^{1-p}}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-25,-5,0])
        self.play(Write(text3))
        text4 = Tex(
                    r"\text{等价于}$\dfrac{\ln x}{x^{1-p}}$",color=PURPLE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,-5,0])
        self.play(Write(text4))
        rectangle=Rectangle(color=BLUE,fill_opacity=0.0,width=13,height=8
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle.move_to([-10, -5, 0])
        self.play(Create(rectangle))
        #画曲线
        curve = CustomCurve(color=RED, stroke_width=20)
        
        # 添加到场景并播放动画
        self.play(Create(curve))
        self.wait(0.5)





        text5 = Tex(
                    r"$1-p>1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([13, 3, 0])
        
        text6 = Tex(
                    r"$1-p=1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([13,-5,0])
        text7 = Tex(
                    r"$1-p<1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([13,-13,0])
        
        text8 = Tex(
                    r"$x\gg \ln x$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([-20,-15,0])



        self.play(Write(text5),Write(text6),Write(text7))

        self.play(Write(text8))

        text9 = Tex(
                    r"\text{与}$\dfrac{1}{x^{1-p}}$\text{同趋势}",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([27, 3, 0])
        self.play(Write(text9))
        text11 = Tex(
                    r"\text{(发散)}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([40,3,0])
        self.play(Write(text11))

        text12 = Tex(
                    r"\text{与}$\dfrac{1}{x^{1-p}}$\text{同趋势}",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([27, -13, 0])
        self.play(Write(text12),FadeOut(text8))
        text13 = Tex(
                    r"\text{(收敛)}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([40,-13,0])
        self.play(Write(text13))
        
        text14 = Tex(
                    r"$\int _{0}^{1}\ln xdx$",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        self.play(Write(text14))
        text15 = Tex(
                    r"$\int _{0}^{1}\ln xd\ln x$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        text16 = Tex(
                    r"$\int ^{0}_{-\infty }tdt$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        self.play(
            ReplacementTransform(text14,text15)
        )
        self.wait(0.5)
        self.play(
            
            ReplacementTransform(text15,text16)
        )
        text17 = Tex(
                    r"$\text{(发散)}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,-15,0])
        self.play(Write(text17))
        self.wait(0.5)
        text18 = Tex(
                    r"$\text{(发散)}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([30,-5,0])
        self.play(Write(text18))
        text19 = Tex(
                    r"$p>0$",color=PURE_GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,8,0])
        self.play(Write(text19))

        #半透明矩阵扩展
        rectangle4=Rectangle(color=GREEN,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-22,8,0])
        self.play(
            rectangle4.animate.stretch(16.0,dim=0)
        )









        self.wait()
